💻 bioinformatics

SFUMATO: Bayesian probabilistic clustering for uncertainty-aware spatialtranscriptomics analysis and mapping

SFUMATO is a GPU-accelerated Bayesian probabilistic framework that overcomes the limitations of hard-label clustering in spatial transcriptomics by generating uncertainty-aware, color-blended visualizations and quantitative maps that capture gradual transcriptional transitions and tissue heterogeneity without requiring prior cell segmentation.

Original authors: Giustolisi, A., Avenel, C., Wählby, C.

Published 2026-10-01

📖 7 min read🧠 Deep dive

CC BY 4.0

Original authors: Giustolisi, A., Avenel, C., Wählby, C.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

In the quiet corners of a microscope slide, a new kind of map is being drawn, one that reveals the hidden architecture of life within a tissue. For decades, scientists have studied cells by cutting them apart, counting them, and sorting them into neat categories, much like a librarian organizing books by genre. This approach works well when the goal is to know exactly how many of each type of cell exists. However, living tissue is rarely so tidy. Cells often blend into one another, changing their behavior gradually as they move from one region to another, or mixing their signals in ways that defy simple labels. To understand these complex, shifting landscapes, researchers need a way to see the tissue not as a collection of distinct islands, but as a continuous terrain where boundaries are often soft and uncertain.

This is the challenge that a team of researchers at Uppsala University in Sweden has tackled with a new method called SFUMATO. By analyzing the genetic instructions inside cells without first trying to draw the outlines of those cells, they have created a way to visualize tissue that captures both sharp divisions and gentle transitions. Their work, published recently, offers a fresh perspective on how we see the microscopic world, moving away from rigid boxes and toward a more fluid, realistic picture of biological complexity.

The researchers began with data from a powerful technology known as in situ sequencing. Imagine a camera that can take a picture of a tissue sample and, instead of just showing colors, records the specific genetic messages being sent by thousands of individual molecules at precise locations. These molecules, called transcripts, act as the cell's active instructions. In a single sample, there can be tens of millions of these messages scattered across the tissue. The challenge for scientists has been to make sense of this massive cloud of data. Traditional methods usually try to first identify every single cell, draw a line around it, and then decide what kind of cell it is. But this process is fragile; if the line is drawn incorrectly, or if cells are stuck together, the entire analysis can be skewed. Furthermore, forcing a sharp line between two areas that are actually blending together can hide important biological truths.

To solve this, the team developed SFUMATO, a tool that skips the step of drawing cell boundaries entirely. Instead of looking for individual cells, the software looks at the genetic signals in small, overlapping patches of the tissue. It treats the data as a continuous flow of information rather than a list of separate items. The method uses a statistical approach to group these patches based on how similar their genetic messages are. Crucially, it does not force each patch into a single, rigid category. Instead, it calculates the likelihood that a patch belongs to different groups at the same time. This allows the software to recognize when a region is a mix of two different types of tissue, or when a transition is happening gradually.

The result is a map that looks like a painting rather than a coloring book. The researchers named their method after a technique used by Renaissance painters, where subtle shifts in tone are used to soften edges and create a sense of depth. In these new maps, areas that are genetically similar are given similar colors, while areas that are very different are given contrasting colors. Where two types of tissue meet, the colors blend smoothly, showing the viewer exactly where the uncertainty lies. If a patch of tissue is clearly one type, it appears as a solid color. If it is a mix, the colors merge, creating a gradient that reveals the complexity of the transition. This visual approach allows scientists to see not just where one type of tissue ends and another begins, but how they change into one another.

The team tested this method on two very different biological landscapes: the brain of a mouse and a sample of human breast cancer. In the mouse brain, they compared their new maps to existing methods that rely on drawing cell outlines. They found that their approach could identify the same major cell types and tissue structures, but with a much clearer view of the boundaries. In areas where the tissue changed gradually, the traditional maps showed abrupt, artificial lines that did not reflect reality. The new maps, however, showed a smooth flow of color, accurately representing the gradual shift in genetic activity. This was particularly useful in identifying regions where different cell types were intermingling, a detail that was often lost or distorted in older methods.

In the human breast cancer samples, the method proved its ability to find disease-related structures without needing to know where the cells were. The researchers were able to distinguish between invasive cancer, which spreads into surrounding tissue, and a non-invasive form of the disease that stays contained within ducts. The maps generated by the new method matched the descriptions given by pathologists, who had manually examined the tissue under a microscope. The software successfully highlighted the invasive regions and the non-invasive areas, even though it had never seen the cell boundaries that pathologists use to make their diagnosis. This suggests that the genetic organization of the tissue itself contains enough information to define these disease states, independent of the physical shape of the cells.

One of the most significant findings of the study is that the way we count cells might not always be the best way to understand tissue. Traditional methods count how many of each cell type are present, but this can be misleading if the cells are different sizes or if the tissue is packed differently in various areas. The new method measures the area that a specific genetic pattern occupies. This provides a more direct estimate of how much space a particular type of tissue takes up, which can be a more accurate reflection of its role in the body. By focusing on the area rather than the count, the researchers found that their maps could reveal the true spatial organization of the tissue, showing how different regions occupy space and interact with their neighbors.

The researchers also demonstrated that their method is flexible and can be adjusted to show different levels of detail. By changing a single setting, they could zoom out to see the broad organization of the entire tissue or zoom in to see the finer details of specific cell groups. Importantly, when they changed this setting, the colors remained consistent. A region that looked like a specific shade of yellow at a broad level would still be a shade of yellow when zoomed in, just with more detail. This consistency helps scientists navigate complex data without getting confused by sudden, unrelated changes in how the tissue is colored.

This work represents a shift in how scientists visualize and interpret the microscopic world. By moving away from the rigid requirement of defining every cell boundary, the researchers have created a tool that embraces the natural uncertainty and fluidity of biological systems. The maps they produce do not just show where things are; they show how things change, blend, and transition. This approach offers a more honest and nuanced view of tissue organization, one that respects the complexity of life rather than trying to simplify it into neat, separate boxes. As scientists continue to explore the intricate details of the human body, tools like this will be essential for uncovering the subtle patterns that define health and disease.

Technical Summary: SFUMATO

Problem Statement

Spatial transcriptomics technologies, particularly in situ sequencing (ISS) methods like Xenium, generate high-resolution gene expression data while preserving spatial context. However, standard analysis workflows often rely on "hard" clustering, which assigns each spatial location to a single discrete cluster. This approach imposes sharp boundaries between transcriptional domains, failing to capture:

Gradual transitions: Biological patterns often involve smooth gradients rather than abrupt shifts.
Mixed signals: Regions containing multiple cell types or ambiguous transcriptional states are forced into a single label.
Uncertainty: The confidence of cluster assignment is lost, potentially leading to misleading interpretations of tissue organization.
Segmentation dependency: Many methods require prior cell segmentation (often based on nuclear staining), which is error-prone in tissues like cancer where nuclei are poorly defined or cells are fused.

Existing segmentation-free methods either lack a partitioning capability for downstream analysis (e.g., color-based encodings) or rely on probabilistic factorization that requires post-hoc interpretation and may not scale efficiently to millions of transcripts.

Methodology

SFUMATO (Segmentation-Free Uncertainty Mapping and Analysis of Transcriptomic Organisation) is a GPU-accelerated Bayesian probabilistic framework designed to address these limitations. The workflow proceeds through the following stages:

1. Feature Extraction and Preprocessing

SFUMATO adopts a Points2Regions-inspired pipeline to avoid cell segmentation:

Binning: Transcripts are rasterized onto square grids at multiple spatial resolutions.
Aggregation: Class counts from neighboring pixels across resolutions are aggregated using inverse-distance weighted interpolation to create a multi-scale representation of local gene composition.
Normalization: Binned gene counts are log-transformed ( $\log(1+x)$ ) and L1-normalized.
Dimensionality Reduction: Truncated Singular Value Decomposition (TruncatedSVD) is applied to the sparse feature matrix to obtain a low-dimensional latent representation ( $Z$ ). This is preferred over PCA for its ability to handle sparse matrices without densification.

2. Bayesian Gaussian Mixture Model (BGM)

A Bayesian Gaussian Mixture Model is fitted to the latent representation $Z$ :

Variational Inference: The model uses variational inference (implemented in PyTorch for GPU acceleration) to approximate posterior distributions over mixture weights, means, and covariances, rather than relying on point estimates or MCMC sampling.
Diagonal Covariance: To ensure computational tractability for large datasets (millions of bins), diagonal covariance matrices are assumed, decoupling dimension estimation.
Overclustering: The model is fitted with a number of components ( $K_{BGM}$ ) larger than the user's target number of clusters ( $K$ ), typically $K_{BGM} = \lceil 1.5 \times \max(K) \rceil$ . This "overclustering" strategy captures fine-grained transcriptional states before merging.

3. Hierarchical Merging and Color Assignment

Dendrogram Construction: Soft centroids for the overclustered components are computed based on posterior responsibilities. An agglomerative hierarchical clustering is performed on these centroids using complete linkage and optimal leaf ordering.
Hierarchical Consistency: When a user requests a specific number of clusters $K$ , the shared dendrogram is cut at that level. This ensures that changing $K$ refines the same hierarchical representation rather than generating unrelated categorical maps.
Color Mapping: Clusters are assigned colors based on their position in the dendrogram. Neighboring clusters in the expression-based hierarchy receive similar colors, while distant branches receive contrasting colors.

4. Probabilistic Color Mixing

Instead of assigning a single hard label, SFUMATO visualizes uncertainty through color blending:

For each spatial bin, the two most probable components are identified.
Their assigned colors are blended using a logarithmic weighting function: $c_i = \frac{\log(1 + \alpha r_{i1}) c_1 + \log(1 + \alpha r_{i2}) c_2}{\log(1 + \alpha r_{i1}) + \log(1 + \alpha r_{i2})}$ , where $r$ represents posterior probabilities and $\alpha=50$ .
This results in smooth color transitions for ambiguous regions and distinct colors for high-confidence assignments.

5. Semantic Segmentation and Quantification

Posterior probability maps can be converted into binary semantic masks using morphological reconstruction with high and low probability thresholds. This allows for the quantitative estimation of area fractions for transcript-defined tissue components, aligning with the Delesse principle (where area fraction estimates volume fraction).

Key Contributions

Segmentation-Free Visualization: SFUMATO provides an efficient representation of transcript-level spatial data without requiring prior cell segmentation. It links color assignment to the expression-based hierarchy, ensuring that color similarity reflects transcriptional similarity.
Hierarchically Consistent Visualization: By deriving multiple clustering resolutions from a single overclustered probabilistic model and a shared dendrogram, SFUMATO ensures that visualizations remain stable and consistent as the number of clusters ( $K$ ) varies.
Probabilistic Clustering for Semantic Segmentation: The framework retains posterior probabilities to derive semantic regions at both cell-associated and niche scales. It supports the conversion of these probabilities into semantic masks for comparison with pathology annotations, independent of cell segmentation.
Uncertainty-Aware Representation: Through probabilistic color mixing, SFUMATO explicitly visualizes transition zones and mixed transcriptional states, avoiding the artificial boundaries imposed by hard clustering.

Results

The authors evaluated SFUMATO on two public Xenium datasets: a mouse brain section and a human breast cancer section.

Mouse Brain (Cell Scale):
- SFUMATO demonstrated substantial agreement with segmentation-free methods (Points2Regions, FICTURE) and the 10x Genomics graph-based reference cell typing.
- Many-to-one correspondences between SFUMATO clusters and reference cell types were observed, but these involved transcriptionally related clusters with similar colors, indicating that SFUMATO captures a finer, continuous hierarchy.
- SFUMATO successfully recovered major cell populations without cell segmentation, even in regions lacking detectable DAPI signals where segmentation-based methods failed.
- The method preserved local transcriptional similarity, with color gradients accurately reflecting gradual transitions in tissue organization.
Mouse Brain (Niche Scale):
- Across varying cluster resolutions ( $K=15$ to $30$), SFUMATO maintained coherent visual organization. Unlike Points2Regions, which produced shifting categorical boundaries, SFUMATO showed gradual color changes in transition zones and consistent sharp contrasts in distinct regions.
Human Breast Cancer:
- Niche Level: SFUMATO-derived semantic masks showed high spatial concordance (Dice score 0.859) with pathology-annotated invasive carcinoma regions. The DCIS-like compartment showed substantial overlap (Dice 0.726) but appeared more heterogeneous and spatially fragmented, suggesting that the targeted transcript panel alone may not fully resolve the specific DCIS subregions defined by multimodal pathology analysis.
- Cell Level: Broad cellular compartments (e.g., invasive tumor, myoepithelial cells) were successfully mapped to SFUMATO components. The method revealed that broad biological compartments often correspond to multiple related SFUMATO clusters, reflecting transcriptional heterogeneity within cell types.

Significance and Claims

The paper claims that SFUMATO offers a unified probabilistic representation of spatial transcriptomics that integrates clustering, visualization, and semantic segmentation. Its primary significance lies in:

Interpretability: By replacing hard assignments with posterior probability distributions, SFUMATO allows biological gradients and mixed states to be visualized directly, rather than suppressed.
Robustness to Segmentation Errors: By operating directly on transcript distributions, it avoids the biases and errors introduced by cell boundary delineation, particularly in complex tissues like cancer.
Quantitative Rigor: The framework provides a principled path to estimating tissue composition via area fractions, which are argued to be more appropriate than cell counts for characterizing spatial occupancy in histological sections.
Scalability: The GPU-accelerated implementation and efficient variational inference make it applicable to datasets containing tens of millions of transcripts.

The authors position SFUMATO not merely as a clustering algorithm, but as a holistic framework where visualization is an integral part of biological interpretation, reflecting the continuous and uncertain nature of biological organization.